you do not have to go out of your way to refute her claims, the truth will come out, rest assured. But of course you do not have to play along with her wording. When somebody asks you, it is probably best that you thank them for their concern and say it is a private matter, which in fact is.
Now is the time to focus on you, your family. Try to eat well and healthy, exercise, get enough sleep. I am sure you can afford to drop some weight, buy some new clothes, reinvent yourself, start an affair with yourself.